Miscible displacements between silicone oils in capillary tubes

Abstract

An experiment in which one viscous silicone oil displaces another more viscous silicone oil in capillary tubes, leading to a version of so-called fingering displacement, is reported here. The fractional volume of the more viscous fluid left on the tube wall after the finger front had passed was measured. This fraction, m, defined as m=1− U m/ U tip, is a critical diagnostic parameter used to identify finger patterns. Here, U m is the mean velocity of the Poiseuille flow ahead the finger front and U tip the propagation speed of the finger tip. In the present case, the fraction m is a function of the Peclet number, Pe, a viscous Atwood number, At, and a gravitational parameter, F. In this experiment, m was obtained by measuring the finger propagation speed, U tip, for a range of injection rates, tube diameters and orientations and fluid viscosities to cover a range of Pe, At and F. For large Pe, the results show the fraction m reached a constant value that depended only on Atwood number. For small Pe, gravitational effects were substantial as measured by the magnitude of F, which is the ratio of gravitational to viscous effects. In this case m is a function of all three parameters and it becomes possible to interpolate the results to obtain the value of m when gravity is absent.